Question:
The demand function of a light rail transit system (LRTS) of a city is represented as \(Q = 43000 - 850P\), where \(Q\) is the ridership/day and \(P\) is the fare/ride. If the existing fare of Rs. 30 per ride is reduced to Rs. 25 per ride, then the consequent increased ridership of the LRTS (in percentage) is (rounded off to two decimal places).
The demand function of a light rail transit system (LRTS) of a city is represented as \(Q = 43000 - 850P\), where \(Q\) is the ridership/day and \(P\) is the fare/ride. If the existing fare of Rs. 30 per ride is reduced to Rs. 25 per ride, then the consequent increased ridership of the LRTS (in percentage) is (rounded off to two decimal places).
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Find ridership at Rs. 30 and Rs. 25 using \(Q=43000-850P\), then take the percentage change over the original ridership.
Updated On: Jul 16, 2026
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Verified By Collegedunia
Correct Answer: 24.29
Solution and Explanation
Step 1: Understanding the Question.
We are given a linear demand function for a light rail transit (LRTS) system, \(Q = 43000 - 850P\), where \(Q\) is the daily ridership and \(P\) is the fare per ride. We need the percentage rise in ridership when the fare drops from Rs. 30 to Rs. 25.
Step 2: Find the ridership at the original fare.
Put \(P = 30\) into the demand function:
\[ Q_1 = 43000 - 850(30) = 43000 - 25500 = 17500 \]
So at Rs. 30 per ride, 17,500 riders use the LRTS each day.
Step 3: Find the ridership at the reduced fare.
Put \(P = 25\) into the demand function:
\[ Q_2 = 43000 - 850(25) = 43000 - 21250 = 21750 \]
So at Rs. 25 per ride, ridership rises to 21,750 riders per day.
Step 4: Work out the percentage increase.
The rise in ridership is:
\[ \Delta Q = Q_2 - Q_1 = 21750 - 17500 = 4250 \]
The percentage increase, measured against the original ridership, is:
\[ \% increase = \frac{\Delta Q}{Q_1} \times 100 = \frac{4250}{17500} \times 100 = 24.2857\ldots\% \]
Final Answer:
Rounded off to two decimal places, the ridership increases by about 24.29%, which sits inside the accepted range of 24.00% to 25.00%.
\[ \boxed{24.29\%} \]
We are given a linear demand function for a light rail transit (LRTS) system, \(Q = 43000 - 850P\), where \(Q\) is the daily ridership and \(P\) is the fare per ride. We need the percentage rise in ridership when the fare drops from Rs. 30 to Rs. 25.
Step 2: Find the ridership at the original fare.
Put \(P = 30\) into the demand function:
\[ Q_1 = 43000 - 850(30) = 43000 - 25500 = 17500 \]
So at Rs. 30 per ride, 17,500 riders use the LRTS each day.
Step 3: Find the ridership at the reduced fare.
Put \(P = 25\) into the demand function:
\[ Q_2 = 43000 - 850(25) = 43000 - 21250 = 21750 \]
So at Rs. 25 per ride, ridership rises to 21,750 riders per day.
Step 4: Work out the percentage increase.
The rise in ridership is:
\[ \Delta Q = Q_2 - Q_1 = 21750 - 17500 = 4250 \]
The percentage increase, measured against the original ridership, is:
\[ \% increase = \frac{\Delta Q}{Q_1} \times 100 = \frac{4250}{17500} \times 100 = 24.2857\ldots\% \]
Final Answer:
Rounded off to two decimal places, the ridership increases by about 24.29%, which sits inside the accepted range of 24.00% to 25.00%.
\[ \boxed{24.29\%} \]
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